This Google Search makes me think the song is quite well-known, but I can't find the lyrics. I'm sure if you watch this thread, somebody will post the song. The most interesting entry was this one (click) from a book called The Companion to Irish Music, by Fintan Vallely:

Peter Vallelly (1926-    ). Singer. Born Derrynoose, County Armagh. Reared by his mother, a singer, he picked up songs at house sessions and dances in childhood, but particularly from aunt Kate McAtavey (nee Mooney) - from whom he got 'The Banks of the Callan' - and uncle John Mooney from whom he got 'At the Foot of Newry Mountains.' Neighbour Sarah Makem was also a big influence. He recorded for RE with Ciaran MacMathuna in 1956, and with Johnny Pickering's Ceili Band. His daughter Patricia plays fiddle and sings professionally.

Theree's a Banks of the Callan CD, a collection of traditional songs from County Armagh. "Banks of the Callan (Keady Town)" has also been recorded by Pat Woods, who calls himself "The Bard of Armagh" (and who apparently has recorded a Jerry Rasmussen song).

Also note this:

Callan River is a river in County Armagh, Northern Ireland which joins the River Blackwater 1.6 km upstream from Bond's Bridge. It is navigable by dinghy or canoe for 2 km to Fairlawn Bridge. It flows in a generally northerly direction from Tullnawood lake, past Darkley, passing within a few miles of Keady town, through Tassagh and on to Armagh. The Callan River, flowing by the city of Armagh, and the Tall River, running by Richhill, join together, and the united steam enters the Blackwater one mile below Charlemont[1]

The area upstream of Armagh has many former linen mills that were built to use the waterpower of the river. There is also a viaduct at Tassagh that once carried the railway line from Armagh to Keady.

-Joe-